I play with a castle DM screen that has dice towers which dump in front of and behind my screen. When the players won't immediately know if their skill check succeeded (Insight for example), they roll in the tower and I see the result. (I also have across the bottom of the tower where a die can be rolled under the screen to me, then I flick it back out.)
When we play over a VTT (Fantasy Grounds) we use the built in dice tower. They drop their roll there, they see a shadow of their dice rolling, and I see the result.
It's not because I'm concerned about them meta-gaming--it's because it adds uncertainty that *we all want*. When I'm playing instead of DMing (rare, but it happens) I actually prefer to not know the result of my Insight check. If I roll a 1 or a 3, I know that my skill check was worthless. I can RP it accordingly--but I know that I failed my Insight check, and now I will be conflicted about further questioning. Would I be pressing this issue if I didn't know I failed the last check? Maybe--maybe not.
I'm even fine with the DM rolling behind his screen if a tower isn't available.
I also get just having the player roll, because it's more convenient, and not everyone has sweet-ass dice tower screens to use. If I say want to know if the guy I'm talking to is sincere and there's a die roll then the DM says, "He seems to be genuine," my next action isn't biased by me as a player. If I see the die come up a 1 and get the same response, my "RP" response should be to accept that this guy is telling the truth and move on, even if it seems fishy to me.
EDIT: Oh yeah, it also lets me fudge a successful check when stupid ass barbarian is the only one that stopped murder-hoboing long enough to look for a clue as to who is pulling the strings behind the scenes. I figured that 10 DC would ensure the guys with Investigation would find the clues, but now I want to reward HULK-SMASH for thinking for a few minutes, even if it's just because he wants to know where more people to kill and take their gold are hiding.